ETFs and funds

What a fund is

A fund is pooled capital: thousands of investors hand money to one legal vehicle, which buys a portfolio of assets and issues shares of itself back to the investors. You own a slice of the pool, not the underlying stocks directly.

The pool's per-share value is the NAV (net asset value):

$\text{NAV} = \frac{\text{market value of holdings} - \text{liabilities}}{\text{fund shares outstanding}}$

Why pool at all? Diversification you couldn't afford alone (owning all 500 S&P names yourself means 500 positions and constant rebalancing), professional administration, and — historically — access. For a quant, funds also matter as instruments: SPY is the workhorse asset in half the backtests you'll ever run.

Mutual funds vs. ETFs

Both are pooled funds. The difference is the trading plumbing:

A mutual fund order placed at 10am and one placed at 3:59pm get the same price: NAV computed after the 4pm close. An ETF trades intraday at a market price that can, in principle, drift away from NAV. Which raises the obvious question —

Why does the ETF price stay glued to NAV?

Nobody decrees it. Arbitrage enforces it. A small set of institutional firms called authorized participants (APs) can transact with the ETF issuer in a way you and I can't:

• Creation: hand the issuer a basket of the underlying stocks, receive newly created ETF shares.
• Redemption: hand back ETF shares, receive the underlying basket.

Suppose SPY trades at $500.50 while its underlying basket is worth$500.00. An AP buys the basket for 500.00, delivers it for new SPY shares, sells those at 500.50, and pockets ~0.50 per share, risk-free. That selling pushes SPY's price back down toward NAV. If SPY trades below NAV, the AP runs the machine in reverse. In liquid ETFs this keeps price within a few hundredths of a percent of NAV. (In stressed or illiquid markets — some bond ETFs in March 2020 — gaps can temporarily widen. The arbitrage needs a functioning market in the underlying to work.)

This mechanism is why an ETF quote is trustworthy in a way a closed-end fund's isn't, and it's a beautiful real-world example of the arbitrage arguments you'll meet throughout this curriculum.

Index funds: why SPY tracks the S&P 500

An index fund doesn't pick stocks. It holds the constituents of a published index — for SPY, the S&P 500 — at index weights, mechanically buying and selling only when the index itself changes. No analysts, no forecasts, near-zero turnover. That's why the fee can be tiny: SPY charges about 0.09% per year, and the cheapest S&P 500 ETFs charge 0.02–0.03%.

The fund won't match the index exactly — fees, cash drag, and rebalancing friction create tracking error, the standard deviation of the fund-minus-index return difference. For giant S&P 500 funds it's a rounding error; for exotic index products it's worth checking.

The expense ratio: the fee that compounds

The expense ratio is deducted from fund assets continuously — you never see a bill, which is exactly why it's underrated. From B1-07 you know what an exponent does over 30 years:

• 8% gross, no fee: $1.08^{30} \approx 10.06\times$
• 8% gross, 1% fee (net 7%): $1.07^{30} \approx 7.61\times$
• Ratio: $7.61 / 10.06 \approx 0.756$

A 1% annual fee consumed about 24% of your final wealth. Not 1% — a quarter. The fee is charged on your whole balance every year, and every dollar it takes also forfeits all its future compounding. Bogle called this "the tyranny of compounding costs," and it's arithmetic, not opinion.

Active vs. passive: what the evidence says

Active funds employ managers to beat the index — and charge accordingly (often 0.5–1%+ vs. 0.03–0.10% for index funds). Do they earn it? The SPIVA scorecard (S&P's long-running study) answers with monotonous consistency: over 15-year windows, roughly nine in ten US large-cap active funds underperform the S&P 500 after fees. Some managers win over short stretches, but persistence is weak — past winners are barely more likely than chance to keep winning.

This shouldn't surprise you. Active managers largely are the market, so before costs they collectively earn the market return; after costs they must collectively lag it. Beating the index is a zero-sum game played against other professionals, minus fees. This is precisely the hurdle you take on as a quant — with the honesty to know most participants fail to clear it.

Choosing a fund: the four-item checklist

1. Fee (expense ratio). The most reliable predictor of long-run fund performance is a low fee.
2. Tracking error. Does it actually deliver the index?
3. Liquidity. Tight bid–ask spread and healthy daily volume — you pay the spread on every trade (B1-03's lesson applies to ETFs too).
4. AUM. Very small funds (roughly under $100M) earn little fee revenue and get closed and liquidated more often — a taxable annoyance, not a loss, but worth avoiding.

Summarize this lesson in your own words

Write 3–5 sentences covering: what a fund is, how ETFs differ from mutual funds, what keeps ETF price near NAV, and why fees matter far more than they look. Don't peek — then compare against the lesson.